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The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
The nines' complement of a number given in decimal representation is formed by replacing each digit with nine minus that digit. To subtract a decimal number y (the subtrahend) from another number x (the minuend) two methods may be used: In the first method, the nines' complement of x is added to y. Then the nines' complement of the result ...
Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, [1] and more generally, fixed point binary values. Two's complement uses the binary digit with the greatest value as the sign to indicate whether the binary number is positive or negative; when the most significant bit is 1 the number is signed as negative and when the most ...
For instance, a two's-complement addition of 127 and −128 gives the same binary bit pattern as an unsigned addition of 127 and 128, as can be seen from the 8-bit two's complement table. An easier method to get the negation of a number in two's complement is as follows:
Some of the related mathematical skills necessary for solving word problems are mathematical vocabulary and reading comprehension. This can again be connected to the example above. With an understanding of the word "spent" and the concept of subtraction, it can be deduced that this word problem is relating the two. [2]
A word equation is a formal equality:= = between a pair of words and , each over an alphabet comprising both constants (c.f. ) and unknowns (c.f. ). [1] An assignment of constant words to the unknowns of is said to solve if it maps both sides of to identical words.
The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".
A Graeco-Latin square or Euler square or pair of orthogonal Latin squares of order n over two sets S and T (which may be the same), each consisting of n symbols, is an n × n arrangement of cells, each cell containing an ordered pair (s, t), where s is in S and t is in T, such that every row and every column contains each element of S and each element of T exactly once, and that no two cells ...